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--- duke_notes [2025/11/10 20:36] – admin
+++ duke_notes [2025/11/17 21:46] (current) – admin
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 [[https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./06%3A_Inference_for_Categorical_Data | Inference for Categorical Variables]]
-  * Parametric One-Sample Inference of Categorical Variables
+===== General Tips =====
-    * one-sample proportion test
-    * $\Chi^2$ goodness of fit test
+  * if you can, pick a continuous outcome over a binary outcome
+    * Why? For a binary outcome, you'll need a much larger sample size. Continuous outcomes also allow more precision.
+  * logistic regressions stink!
+logistic regression = linear model for the log-odds of the outcome
+=== analyzing relationship between categorical outcome and a continuous covariate ===
+===effect modification vs confounding===
+if we don't take effect modification into account, we get an over-generalized estimate of the relationship between the outcome and the exposure for the entire co-hort
+  * Breslow-Day Test examines if evidence of a differential association between two variables across the level of a third variable
+    * similar limitations to Cochran-Mantel-Haenszel test
+==== Cochran-Mantel_haenszel test ====
+  * limitations
+    * can only adjust for one variable at a time
+looks at two binary categorical variables while adjusting for the value of a third categorical variable
+==== Parametric One-Sample Inference of Categorical Variables====
+  * one-sample proportion test
+    * do NOT use Yate's continuity, so specify:
+      * prop.test(..., correct = FALSE)
+  * $\Chi^2$ goodness of fit test
+    * to ensure sufficient sample size: $n \cdotp_{0} > 5$
+    * don't use continunity corrections!
+      * chisq.test(..., correct = FALSE)
+**NOTE**: //one-sample single proportion test// gives a 95% CI -- $\Chi^2$ does not!
+==== Types of Probabilites ===
+[[https://sites.nicholas.duke.edu/statsreview/jmc/ | Joint, Marginal and Conditional Probabilities]]
   * QI

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